(Solved): 3. Maclaurin series for the function sinx is given by sinx=x3!x3+5!x57!x7+ a) St ...

3. Maclaurin series for the function $\sin x$ is given by $\sin x=x?\frac{x^3}{3!}+\frac{x^5}{5!}?\frac{x^7}{7!}+?$ a) Starting from the given formula, find the Maclaurin series for $\cos x$ $\cos x=$ b) Calculate ${?}_{0.01}^{0.1}\frac{\sin x}{x}$ with the precision of at least 3 decimal places ( 3 digits after decimal point, _._._- must be correct) (Show all work)